Define a sequence (an) recursively by setting a1 = V2 and an+1 = v2+ an for n > 1. (a) Show that an < 2 for all n. (b) Show that (an) is monotone, and use this to conclude that (an) converges. (c) Show that an → 2.
Define a sequence (an) recursively by setting a1 = V2 and an+1 = v2+ an for n > 1. (a) Show that an < 2 for all n. (b) Show that (an) is monotone, and use this to conclude that (an) converges. (c) Show that an → 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Define a sequence (an) recursively by setting a1 =
V2 and an+1 = v2+ an for n > 1.
(a) Show that an < 2 for all n.
(b) Show that (an) is monotone, and use this to conclude that (an) converges.
(c) Show that an → 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2F8336e90d-9f18-49d2-a7e1-3a59f529e1f0%2F25ej69c_processed.png&w=3840&q=75)
Transcribed Image Text:Define a sequence (an) recursively by setting a1 =
V2 and an+1 = v2+ an for n > 1.
(a) Show that an < 2 for all n.
(b) Show that (an) is monotone, and use this to conclude that (an) converges.
(c) Show that an → 2.
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